# Compare weighted and unweighted mean temperature¶

Author: Mathias Hauser

We use the air_temperature example dataset to calculate the area-weighted temperature over its domain. This dataset has a regular latitude/ longitude grid, thus the grid cell area decreases towards the pole. For this grid we can use the cosine of the latitude as proxy for the grid cell area.

In [ ]:
%matplotlib inline

import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import numpy as np

import xarray as xr


### Data¶

Load the data, convert to celsius, and resample to daily values

In [ ]:
ds = xr.tutorial.load_dataset("air_temperature")

# to celsius
air = ds.air - 273.15

# resample from 6-hourly to daily values
air = air.resample(time="D").mean()

air


Plot the first timestep:

In [ ]:
projection = ccrs.LambertConformal(central_longitude=-95, central_latitude=45)

f, ax = plt.subplots(subplot_kw=dict(projection=projection))

air.isel(time=0).plot(transform=ccrs.PlateCarree(), cbar_kwargs=dict(shrink=0.7))
ax.coastlines()


### Creating weights¶

For a rectangular grid the cosine of the latitude is proportional to the grid cell area.

In [ ]:
weights = np.cos(np.deg2rad(air.lat))
weights.name = "weights"
weights


### Weighted mean¶

In [ ]:
air_weighted = air.weighted(weights)
air_weighted

In [ ]:
weighted_mean = air_weighted.mean(("lon", "lat"))
weighted_mean


### Plot: comparison with unweighted mean¶

Note how the weighted mean temperature is higher than the unweighted.

In [ ]:
weighted_mean.plot(label="weighted")
air.mean(("lon", "lat")).plot(label="unweighted")

plt.legend()